Categorical Equivalence Between $$\varvec{PMV}_{\varvec{f}}$$ PMV f -Product Algebras and Semi-Low $$\varvec{f}_{\varvec{u}}$$ f u -Rings

Studia Logica - An explicit categorical equivalence is defined between a proper subvariety of the class of $${ PMV}$$ -algebras, as defined by Di Nola and Dvure?enskij, to be called $${...     

An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC

Studia Logica - The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency $$\mathsf {mbC}$$ . As a proof-theoretical basis we employ the...     

Two Maximality Results for the Lattice of Extensions of $$\vdash _{\mathbf {RM}}$$

Studia Logica - We use an algebraic argument to prove that there are exactly two premaximal extensions of $$\mathbf {RM}$$ ’s consequence. We also show that one of these extensions is the...     

Modal Companions of $$K4^{+}$$

Studia Logica - We study modal companions of $$K4^+$$ , the strictly positive fragment of K4. We partially find the boundary between all normal extensions of K4 and modal companions of $$K4^+$$...     

Adaptive logics using the minimal abnormality strategy are $$\Pi^1_1$$ -complex

In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is -complete. So, the complexity results in (Horsten and Welch, Synthese 158:41–60, 2007) are mistaken for adaptive logics using the minimal abnormality strategy.     

Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset

Psychometrika - Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The $$\varvec{Q}$$ matrix, which...     

Sequent Calculi for $${\mathsf {}}$$

In this paper we are applying certain strategy described by Negri and Von Plato (Bull Symb Log 4(04):418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.     

The Balanced Pseudocomplemented Ockham Algebras with the Strong Endomorphism Kernel Property

Studia Logica - An endomorphism on an algebra $${\mathcal {A}}$$ is said to be strong if it is compatible with every congruence on $${\mathcal {A}}$$ ; and $${\mathcal {A}}$$ is said to have the...     

Arithmetical Completeness Theorem for Modal Logic $$\mathsf{}$$

We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \(\Sigma _2\) provability predicate of T whose provability logic is precisely the modal logic \(\mathsf{K}\). For this purpose, we introduce a new bimodal logic \(\mathsf{GLK}\), and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \(\mathsf{GLK}\).     

Intermediate Logics Admitting a Structural Hypersequent Calculus

Studia Logica - We characterise the intermediate logics which admit a cut-free hypersequent calculus of the form $$\mathbf {HLJ} + \mathscr {R}$$ , where $$\mathbf {HLJ}$$ is the hypersequent...     

Simplified Kripke-Style Semantics for Some Normal Modal Logics

Studia Logica - Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics $$\mathrm {K45}$$, $$\mathrm {KB4}$$ ($$=\mathrm...     

$${\in_K}$$: a Non-Fregean Logic of Explicit Knowledge

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \({\in_K}\) (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K _i φ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \({\in_K}\) and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \({\in_K}\). Every specific \({\in_K}\)-logic is defined as a certain extension of some underlying classical abstract logic.     

A Deterministic Weakening of Belnap–Dunn Logic

Studia Logica - A deterministic weakening $$\mathsf {DW}$$ of the Belnap–Dunn four-valued logic $$\mathsf {BD}$$ is introduced to formalize the acceptance and rejection of a proposition at a...     

Containment Logics: Algebraic Completeness and Axiomatization

Studia Logica - The paper studies the containment companion (or, right variable inclusion companion) of a logic $$\vdash $$ . This consists of the consequence relation $$\vdash ^{r}$$ which...     

Countably Many Weakenings of Belnap–Dunn Logic

Studia Logica - Every Berman’s variety $$\mathbb {K}_p^q$$ which is the subvariety of Ockham algebras defined by the equation $${\sim ^{2p+q}}a = {\sim ^q}a$$ ($$p\ge 1$$ and $$q\ge 0$$)...     

A Propositional Dynamic Logic for Instantial Neighborhood Semantics

Studia Logica - We propose a new perspective on logics of computation by combining instantial neighborhood logic $$\mathsf {INL}$$ with bisimulation safe operations adapted from $$\mathsf {PDL}$$ ....     

A General Framework for $$ {FDE}$$ FDE -Based Modal Logics

We develop a general theory of FDE-based modal logics. Our framework takes into account the four-valued nature of FDE by considering four partially defined modal operators corresponding to conditions for verifying and falsifying modal necessity and possibility operators. The theory comes with a uniform characterization for all obtained systems in terms of FDE-style formula-formula sequents. We also develop some correspondence theory and show how Hilbert-style axiom systems can be obtained in appropriate cases. Finally, we outline how different systems from the literature can be expressed in our framework.

     

Correction to: The Hahn Embedding Theorem for a Class of Residuated Semigroups

Studia Logica - Let $${\mathcal {O}}$$ be the class of odd involutive $$\hbox {FL}_e$$ -chains which admit finitely many idempotent elements. The price for describing the structure of such a rich...     

A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial solution to the paradox of analysis. Presented by Jacek Malinowski